If $A$ is symmetric and nonsingular, with decomposition $A=LDM^T$, $L$ and $M$ is unit lower triangular, $D$ is diagonal matrix, show that $M=L$.

Asked Sep 26 '15 at 17:45

Active Sep 15 '21 at 22:21

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Let $A$ be a symmetric, non-singular matrix with decomposition $A=LDM^T$, $L$ and $M$ are unit lower triangular, and $D$ is diagonal matrix. Show that $M=L$.

Can I prove $LM^T=(ML^T)^T$ then $M=L$?

edited Sep 15 '21 at 22:21

jbenoit

asked Sep 26 '15 at 17:45

Kevin

2

Are you assuming $A=A^T$? If yes then add it to the problem description. If no then $M=L$ is not true. – A.Γ. Sep 26 '15 at 18:34
Thank you. Yes assuming A is symmetric matrix. – Kevin Sep 26 '15 at 19:08
@Kevin Could you, please, add the condition $A=A^T$ to your problem statement? Otherwise it is not clear for those who miss reading the comment. My answer to other question (see the link) could be of some help. – A.Γ. Sep 26 '15 at 19:56

If $A$ is symmetric and nonsingular, with decomposition $A=LDM^T$, $L$ and $M$ is unit lower triangular, $D$ is diagonal matrix, show that $M=L$.

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